Assigning shortcut for Alt + Ctrl + C doesn't work
&#9096; Ctrl&#9095; AltC isn't working as another shortcut is assigned to it and is used before the set origin shortcut - it will clear constraints, so you probably didn't notice anything happening.



If you untick the Clear Object Constraints shortcut you will be able to use &#9096; Ctrl&#9095; AltC.

As shown above there are several groups that a shortcut may belong to, blender goes through each group and uses the first match found. Fairly sure the search order is the same as what is displayed in the input preferences. You can have some duplication as some groups will not match the current context, for example the clear Pose Constraints shortcut will not match unless you are posing an armature.